Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Foreword; Introduction I. Set Theory 1 9. The notation and terminology of set theory 10 16. Mappings 17 19. Equivalence relations 20 25. Properties of natural numbers II. Group Theory 26 29. Definition of group structure 30 34. Examples of group structure 35 44. Subgroups and cosets 45 52. Conjugacy, normal subgroups, and quotient groups 53 59. The Sylow theorems 60 70. Group homomorphism and isomorphism 71 75. Normal and composition series 76 86. The Symmetric groups III. Field Theory 87 89. Definition and examples of field structure 90 95. Vector spaces, bases, and dimension 96 97. Extension fields 98 107. Polynomials 108 114. Algebraic extensions 115 121. Constructions with straightedge and compass IV. Galois Theory 122 126. Automorphisms 127 138. Galois extensions 139 149. Solvability of equations by radicals V. Ring Theory 150 156. Definition and examples of ring structure 157 168. Ideals 169 175. Unique factorization VI. Classical Ideal Theory 176 179. Fields of fractions 180 187. Dedekind domains 188 191. Integral extensions 192 198. Algebraic integers Bibliography; Index
Foreword; Introduction I. Set Theory 1 9. The notation and terminology of set theory 10 16. Mappings 17 19. Equivalence relations 20 25. Properties of natural numbers II. Group Theory 26 29. Definition of group structure 30 34. Examples of group structure 35 44. Subgroups and cosets 45 52. Conjugacy, normal subgroups, and quotient groups 53 59. The Sylow theorems 60 70. Group homomorphism and isomorphism 71 75. Normal and composition series 76 86. The Symmetric groups III. Field Theory 87 89. Definition and examples of field structure 90 95. Vector spaces, bases, and dimension 96 97. Extension fields 98 107. Polynomials 108 114. Algebraic extensions 115 121. Constructions with straightedge and compass IV. Galois Theory 122 126. Automorphisms 127 138. Galois extensions 139 149. Solvability of equations by radicals V. Ring Theory 150 156. Definition and examples of ring structure 157 168. Ideals 169 175. Unique factorization VI. Classical Ideal Theory 176 179. Fields of fractions 180 187. Dedekind domains 188 191. Integral extensions 192 198. Algebraic integers Bibliography; Index
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